Storm surge forecasting method and system based on coupling model

Abstract

The present application belongs to the technical field of convolutional neural network, and relates to a storm surge forecasting method and system based on a coupling model. The system obtains forecasted tide level, wind stress field, pressure field, astronomical tide component and tide level residual under the same tidal phase from the output of a numerical coupling model, and maps them as multi-time and multi-channel samples under the same coastal grid. Convolution constraint information is generated according to the shoreline mask, water-land boundary distance and water depth variation, and is input into a convolutional neural network for shoreline constraint residual learning to obtain a tide level residual correction. Through confidence evaluation and abnormal correction limitation, the correction and the forecasted tide level are fused to generate a storm surge forecasting result of the grid points and representative stations. The system can constrain the influence of land area, missing grid points and cross-land adjacent pairs on residual characteristics, improve the boundary extrapolation and local mutation problems in the near-shore, gulf and estuary areas, and make the forecasting result maintain better spatial continuity and boundary consistency.

Description

Technical Field

[0001] This invention belongs to the field of convolutional neural network technology and relates to a storm surge forecasting method and system based on a coupled model. Background Technology

[0002] Storm surge forecasting typically employs a coupled forecasting workflow based on meteorological forecast data and ocean hydrodynamic calculations. Conventional systems first read input data such as typhoon path, central pressure, near-surface wind field, pressure field, astronomical tides, and open boundary water levels. Then, meteorological grid data is interpolated into the hydrodynamic model grid, driving the two-dimensional or three-dimensional hydrodynamic equations to calculate the storm surge process according to the forecast start time and lead time. For representative coastal stations, the system generally selects grid points from adjacent sea areas in the computational grid, or interpolates the water levels of surrounding grid points to obtain the station's tide forecast value. For coastal area results, the system typically re-rasterizes the model output to generate a water level distribution map. The core of this approach relies on the numerical representation of meteorological forces, tidal boundaries, and water depth topography. Forecast quality is affected by meteorological input errors, grid scale differences, shoreline generalization, and water depth data resolution. Because the meteorological model grid, hydrodynamic grid, and observation stations are not within the same spatial representation system, existing workflows require multiple interpolations, pruning, lead time registration, and missing data filling. The above processing is usually based on general spatial interpolation and a unified time step, which is relatively coarse in representing local geomorphological differences such as bays, estuaries, and meandering coastlines. In offshore areas, the errors caused by grid interpolation and boundary propagation are relatively smooth; in nearshore, bay, estuary, and narrow waterway areas, the land-water boundary and topographic changes have stronger constraints on water rise propagation, and conventional coupled models are prone to local system biases during grid transformation and shoreline generalization.

[0003] To correct coupling forecast biases, existing technologies have incorporated machine learning models into the storm surge forecasting process. A relatively close approach is to use historical coupled model forecast tide levels, measured tide levels, wind speeds, air pressures, astronomical tides, and forecast lead times as samples to train a neural network to learn forecast errors, and then output error corrections during the operational forecasting phase. When using convolutional neural networks, wind, pressure, and tide fields are typically organized into regular grid channels. Spatial features are extracted by convolutional kernels within a fixed window, and after multiple convolutions and nonlinear mappings, a residual field or a corrected tide field is obtained. This type of method can utilize statistical relationships in historical samples, but its convolutional operations usually assume that adjacent grids are spatially continuous. When the convolutional window crosses the land-water boundary, it may still include features of land grid points, missing grid points, or unconnected water areas in the calculation. Some solutions remove land area outputs through masks or prune outliers after training. Other solutions treat near-shore station residuals as independent sequences before interpolating them back into the surface domain result, but these processing methods mostly remain at the level of input processing or output modification. Conventional training objectives typically focus on residual numerical errors, lacking constraints on residual spatial gradients, boundary availability, and real connectivity within water bodies. Masking, site interpolation, and outlier pruning are not involved in convolutional feature formation and training constraints, making it difficult for the network to adhere to real shorelines, abrupt changes in water depth, and water connectivity during the feature extraction stage.

[0004] The main technical problem with existing storm surge forecasting methods that incorporate convolutional neural networks (CNNs) for correction is that regular rasterized inputs and fixed convolutional neighborhoods cannot adequately represent nearshore land-water boundaries, abrupt changes in water depth, and marine connectivity constraints. This leads to inconsistencies between the tidal residual field learned by the neural network and the actual propagation conditions of storm surges in nearshore areas. This problem arises because after the meteorological field, hydrodynamic field, and observation residuals are uniformly rasterized, the original shoreline morphology is discretized into regular grids. The CNN then aggregates features according to fixed neighborhoods, resulting in land-based grid points, boundary transition grid points, missing grid points, and adjacent grid points across land areas potentially participating in the residual feature calculation. When typhoon-induced water level rise approaches the shoreline, enters a bay, or is constrained by estuary topography, the residuals are not ordinary image textures and cannot be simply extrapolated using homogeneous convolutional windows. Because the water level residuals propagate along the real water surface and are constrained by water depth gradients, shoreline inflections, and tidal phases, erroneous neighborhoods alter the network's learning of the residual direction and magnitude. Such errors are more likely to persist in training samples when stations are sparse, observations are incomplete, or shoreline morphology is complex. Without the joint constraints of shoreline masking, boundary distance, water depth gradient, adjacency connectivity, and physical consistency training, residual corrections are prone to boundary expansion, local abrupt changes, and errors in propagating biases near stations, which in turn amplify or transfer existing near-shore errors in the coupled model. Summary of the Invention

[0005] The purpose of this invention is to provide a storm surge forecasting method and system based on a coupled model, which can solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A storm surge forecasting method based on a coupled model includes the following steps:

[0008] Step S1: Obtain the forecast tide level, wind stress field, pressure field, astronomical tide component, and historical tide level residuals under the same tidal phase from the storm surge numerical coupling model, and establish a unified data index and validity identifier.

[0009] Step S2: Map the predicted tide level, wind stress field, air pressure field, historical tide level residuals under the same tidal phase, and astronomical tide components to the same effective coastal sea area grid to construct multi-time multi-channel samples.

[0010] Step S3: Generate constraint information for convolution calculation based on shoreline mask, distance between land and water boundaries, and water depth changes;

[0011] Step S4: Input the multi-time multi-channel samples and the constraint information generated in step S3 for convolution calculation into the convolutional neural network, perform shoreline constraint residual learning, and output the tide level residual correction amount with the same spatial resolution and time index as the predicted tide level.

[0012] Step S5: Generate residual confidence weights based on the completeness of the input samples, the continuity of the residual space, and the similarity of historical errors on the same shore. After anomaly correction constraints are applied to the tide level residual correction, the weights are superimposed on the tide level forecast of the coupled model to generate storm surge forecast results.

[0013] Preferably, step S2 specifically includes: using the effective coastal sea area corresponding to the hydrodynamic calculation grid as the target grid, retaining the water area validity marker and assigning an index identifier to each target grid point; registering the wind stress field, air pressure field, forecast tide level and astronomical tide component with the same time scale according to the forecast start time and forecast lead time; encoding the historical tide level residual, current forecast lead time number and water depth gradient as additional channels, which together with the forecast tide level constitute the input tensor of the convolutional neural network.

[0014] Preferably, step S3 specifically includes: dividing the coastal grid into effective sea area grid points, land area grid points, boundary transition grid points, and missing measurement grid points, and generating a water-land mask code; calculating the normalized distance from each effective sea area grid point to the nearest water-land boundary along the real sea area connectivity path, and generating a boundary sensitive code based on the location of abrupt changes in water depth; and based on the water-land mask code and the boundary sensitive code, masking and reweighting the convolution sampling neighborhood so that the land area grid points and missing measurement grid points do not participate in the residual feature aggregation of the effective sea area grid points.

[0015] Preferably, in step S4, shoreline constraint residual learning specifically includes: performing spatiotemporal joint encoding on multi-time and multi-channel samples to extract shared basic features; using convolutional kernels with different receptive fields to extract residual features corresponding to typhoon-scale external forces, nearshore local water level increases, and tidal phase differences; embedding convolution constraint information into the convolutional kernel weight calculation process, setting the feature responses corresponding to land grid points and missing grid points as non-participating quantities, and finally generating tidal level residual correction quantities.

[0016] Preferably, step S5 specifically includes: calculating residual confidence weights based on the spatial continuity of the residuals output by the convolutional neural network, the similarity of historical errors in the same shore segment, and the completeness of the input samples; limiting the magnitude of the tide level residual correction at low confidence weight grid points, and correcting the residuals at the shoreline boundary transition grid points using the consistency verification results of adjacent effective sea area grid points; and superimposing the limited tide level residual corrections onto the forecast tide level to generate a storm surge forecast result containing grid point forecast values ​​and representative station forecast values.

[0017] Preferably, the training sample construction step of the convolutional neural network includes: forming a sample time window with the start time, maximum water level rise time and water level fall time of the historical storm process; mapping the tide level sequence of different storm processes to training segments with the same phase according to the astronomical tide phase; constructing residual labels with the difference between the measured tide level and the predicted tide level; and setting training masking marks for the land-water boundary, missing measurement time and abnormal observation time.

[0018] Preferably, step S4 further includes a graph convolutional adjacency correction step: constructing an effective sea area grid adjacency matrix based on shoreline connectivity, water depth similarity, and coastal propagation direction; when the regular grid convolutional window crosses land or isolated water areas, replacing cross-land adjacency edges with adjacency edges along the actual water area connectivity path; and performing gating fusion between the regular convolutional features and the graph adjacency features to form a residual feature representation that conforms to the connectivity of nearshore waters.

[0019] Preferably, the training of the convolutional neural network adopts physical consistency constraints, specifically including: smoothing constraints on the residual changes of adjacent effective sea area grid points; setting loss exclusion markers for land area grid points, missing measurement grid points and non-propagable water area grid points; determining the residual gradient penalty weights for different regions based on water depth gradient, shoreline distance and historical extreme water increase distribution, so that the training objective simultaneously constrains residual values, residual spatial changes and boundary validity.

[0020] Preferably, after step S5, an online drift calibration step is also included: according to the consistency of residual direction within the continuous forecast period of the shore segment, the distance between the current input feature distribution and the feature distribution of the historical sample library is calculated; when the consistency of residual direction and the distance of feature distribution simultaneously meet the preset triggering conditions, the shared feature extraction parameters are frozen, and only the local branch parameters of the corresponding shore segment are updated; during the update, matching historical playback samples are selected, and parameter calibration is completed by combining the measured residual labels and the labels selected by confidence screening.

[0021] This invention also provides a storm surge forecasting system based on a coupled model, used to implement the storm surge forecasting method based on the coupled model, the system comprising:

[0022] The coupled forecast input module is used to obtain the forecast tide level, wind stress field, pressure field, astronomical tide component, and historical tide level residuals under the same tidal phase from the storm surge numerical coupling model.

[0023] The spatial uniformity module is used to map the predicted tide level, wind stress field, pressure field, astronomical tide component and historical tide level residuals under the same tidal phase to multi-time multi-channel samples under the same effective coastal sea area grid.

[0024] The shoreline constraint generation module is used to generate convolution constraint information based on the shoreline mask, the distance between the land and water boundaries, and changes in water depth.

[0025] The residual correction module is used to input the multi-time multi-channel samples and convolutional constraint information into the convolutional neural network, perform shoreline constraint residual learning, and obtain the tide level residual correction amount;

[0026] The fusion output module is used to generate residual confidence weights and impose anomaly restrictions on the tide level residual correction, then fuse them with the forecast tide level to output the storm surge forecast result.

[0027] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0028] 1. After adopting the storm surge forecasting system, the forecast tide level, wind stress field, pressure field, astronomical tide component, and historical tide level residuals at the same tidal phase output by the coupled model are mapped to multi-time, multi-channel samples under the same coastal grid. Shoreline masking, land-water boundary distance, and water depth changes are converted into convolutional constraint information and participate in the residual learning process of the convolutional neural network. The convolutional neural network does not directly replace the coupled model in calculating the water level, but outputs a tide level residual correction with the same spatial resolution as the forecast tide level. The storm surge forecast result is then synthesized by the fusion output process and the forecast tide level. Since land grid points, missing grid points, and non-propagating grid points are shielded in feature aggregation and loss calculation, the convolutional sampling neighborhood of the effective nearshore sea area grid points can avoid cross-land propagation paths, and the residual field generation process matches the shoreline boundary, water depth abrupt changes, and sea area connectivity conditions. For areas with meandering coastlines, narrowing bays, and confluences of estuaries, residual corrections are generated according to constrained water neighborhoods, avoiding the introduction of error patterns from the other side of the land or isolated water areas into the current grid point. After residual confidence assessment and anomaly correction constraints, the correction magnitude of low-confidence grid points is constrained, representing the consistency of residual relationships between representative stations and surrounding grid points. This process reduces boundary extrapolation and local abrupt changes caused by regular raster convolution, resulting in better spatial continuity and boundary consistency in tidal level corrections for bays, estuaries, and narrow channels, and reducing the impact of nearshore system bias in coupled models on the final forecast results.

[0029] 2. Beyond the aforementioned main effects, sample construction, graph convolutional adjacency correction, physically consistent training, and online drift calibration further enhance the consistency between model training and runtime phases. Historical storm processes are used to form sample time windows based on their reporting time, maximum rise time, and receding time, and matched according to astronomical tide phases. This ensures that training samples simultaneously encompass the correspondence between storm processes, tidal phases, and coupled model residuals. Adjacency matrices based on shoreline connectivity, water depth similarity, and coastal propagation direction can replace real-world water connectivity paths when regular convolutional windows cross land or isolated water areas, reducing the inclusion of erroneous adjacency relationships in feature representations. Sea area continuity constraints, boundary shielding constraints, and residual gradient constraints incorporate residual values, spatial variations, and boundary availability into the same training objective, reducing the dependence of training results on anomalous observations and missing areas. Residual confidence assessment and anomaly correction constraints constrain the residual amplitude of low-confidence grid points, preventing anomalous outputs from a single grid point from disrupting the continuity of adjacent sea areas. Online drift calibration updates the local branch parameters of the shoreline that meet the triggering conditions. Combined with historical sample playback and high-confidence pseudo-supervision label screening, it can limit the perturbation of the shared feature layer by local updates when there are differences between the new storm process and the historical sample distribution. This allows the correction model to maintain a relatively stable parameter state and output change in continuous forecasts. Attached Figure Description

[0030] Figure 1The flowchart shows the overall processing flow of the storm surge forecasting method based on the coupled model.

[0031] Figure 2 Flowchart for spatial uniformity and multi-temporal multi-channel sample construction;

[0032] Figure 3 Flowchart for shoreline-constrained convolutional residual correction;

[0033] Figure 4 Flowchart for constructing training samples and ensuring physical consistency during training;

[0034] Figure 5 This is a flowchart for online drift calibration and pseudo-supervision screening. Detailed Implementation

[0035] refer to Figure 1 In one embodiment, the storm surge forecasting system based on the coupled model of the present invention is implemented using a data processing program. The system includes a coupled forecast input module, a spatial consistency module, a shoreline constraint generation module, a residual correction module, and a fusion output module. The coupled forecast input module reads the forecast tide level, wind stress field, pressure field, astronomical tide component, and historical tide level residuals under the same tidal phase output by the storm surge numerical coupled model at multiple forecast lead times. The forecast tide level is the water level result calculated by the coupled model based on meteorological driving and tidal boundary. The wind stress field is used to characterize the driving force of the wind field on the sea surface water. The pressure field is used to characterize the water level response corresponding to pressure changes. The astronomical tide component is used to characterize the periodic tidal background. The historical tide level residuals under the same tidal phase are used to characterize the difference between previous forecast values ​​and measured values ​​in the same area under similar tidal phase conditions, and are used to provide phase-matching residual prior information for the current storm surge process. The spatial grid, temporal resolution, and missing data patterns of various types of data are usually different. The coupled forecast input module establishes data source identifiers, forecast start time identifiers, forecast lead time identifiers, and validity identifiers for each type of data to ensure that subsequent processing can distinguish the physical meaning and usability of different data channels.

[0036] In this embodiment, the spatial homogenization module maps the predicted tide level, wind stress field, pressure field, astronomical tide component, and historical tide level residuals under the same tidal phase to multi-time, multi-channel samples under the same coastal grid. The coastal grid uses the effective nearshore sea area corresponding to the hydrodynamic calculation grid as a reference; land areas outside the hydrodynamic grid are not considered as residual output objects. For bays, estuaries, narrow channels, and areas with meandering coastlines, the coastal grid retains the corresponding water area validity markers to avoid treating unconnected water areas as ordinary adjacent areas during the rasterization process. When processing data from different sources, the spatial homogenization module does not directly replace the original meaning with regular image resampling results. Instead, it establishes a set of source grid points for each target grid point and forms a weighted mapping based on spatial distance, time offset, and data validity. The unified data is organized using grid points, timeframes, and channels as indices, with each target grid point corresponding to multiple input channels at each forecast timeframe.

[0037] In practical implementation, the spatial uniformity module can use the following mapping formula to generate the channel values ​​of the target coastal grid:

[0038]

[0039] in, Represents the grid points in the coastal grid of the target. Forecast lead time and data channels The unified input value; Indicates channel The corresponding set of original data source grid points; Represents source grid points To the target grid point The spatial mapping weight is larger when the distance is closer and they belong to the same connected water area; Indicates the time of source data and the forecast lead time of the target. Time registration weights between them; Represents source grid points In the passage The original values ​​in; To prevent stabilization terms with a denominator of 0, the summation operation represents a weighted aggregation of available source grid points, and the division operation represents normalizing the aggregated amount to the channel value of the target grid point. The physical meaning of this formula is to transform data from different grids and timescales into comparable input quantities on the same coastal grid point. For example, the wind stress channel of a target grid point is contributed by two source grid points, with original values ​​of 1.2 and 1.5 respectively. The products of the spatial mapping weight and the temporal registration weight are 0.6 and 0.3 respectively. When the stabilization term takes a very small value, the calculated result is approximately 1.3, indicating that the wind stress input value of the target grid point at that timescale is close to the contribution of the higher-weighted source grid point.

[0040] Table 1 shows the organization method of multi-time, multi-channel samples in this embodiment. This table is used to explain the meaning of fields and processing boundaries of different data before entering the convolutional neural network. In actual implementation, similar channels can be added or reduced according to the output range of the existing coupled model, but each channel needs to have a clear time index, spatial index and validity identifier.

[0041] Table 1. Multi-time, multi-channel sample organization table

[0042]

[0043] Furthermore, the shoreline constraint generation module generates convolutional constraint information based on the shoreline mask, the distance between the land and water boundaries, and water depth variations. The shoreline mask is used to distinguish between effective sea area grid points, land area grid points, and boundary transition grid points; the land-water boundary distance is used to characterize the degree to which sea area grid points are close to the shoreline; and water depth variations are used to characterize the limitation of nearshore topography on the propagation of water level residuals. The shoreline constraint generation module does not treat this information merely as a post-output processing condition, but rather converts it into input constraints during the convolution process, allowing the convolutional neural network to exclude land area grid points and grid points without propagation relationships during the feature extraction stage. For target grid points located at shoreline bends, a regular rectangular convolutional window may contain sea area grid points on the other side of the land area. The shoreline constraint generation module sets the contribution weight of these grid points to a low value or a masked value, while retaining neighboring grid points along the actual water connectivity direction.

[0044] In this embodiment, the residual correction module inputs multi-time, multi-channel samples and convolutional constraint information into a convolutional neural network to obtain the tide level residual correction. The convolutional neural network uses the tide level predicted by the coupled model as a benchmark, and does not directly output the final tide level. Instead, it learns the residual between the measured tide level and the tide level predicted by the coupled model. The input end provides external force, background tide, and historical error features from multi-time, multi-channel samples. The constraint end limits the convolutional neighborhood with shoreline masking, land-water boundary distance, and water depth changes. A shared feature extraction layer is set in the network to form basic spatiotemporal features, a multi-scale residual branch is set to handle typhoon-scale external forces and nearshore local water level differences, and a shoreline constraint convolutional branch is set to introduce boundary constraints in the calculation of convolutional kernel weights. The residual correction output by the convolutional neural network has the same spatial resolution as the predicted tide level, facilitating consistent results between the grid scale and the representative station scale in the fusion output module.

[0045] The fusion output module fuses the tide level residual correction with the forecast tide level to generate the storm surge forecast result. In this embodiment, the fusion does not involve superimposing all grid points with the same amplitude, but rather generates confidence weights based on the spatial continuity of the residuals, the completeness of the input samples, and the similarity of historical errors along the same shoreline. For grid points with complete input and a residual field continuous with the surrounding waters, the residual correction can participate in the synthesis with a higher weight; for grid points located in the shoreline boundary transition zone, with missing input, or with a large number of shielded convolutional neighborhoods, the residual correction participates in the synthesis after amplitude limitation. Its working principle is as follows: the coupled model provides a physically based forecast tide level, the convolutional neural network only learns the systematic residuals of the coupled model in the complex nearshore region, shoreline constraint information restricts the residual propagation path, and the fusion process then performs controlled synthesis of low-confidence residuals. Thus, the forecast result retains the basic water level structure of the coupled model and forms a constrained residual correction in the nearshore boundary region. This embodiment completes a complete data loop from coupled forecast input, spatial uniformity, shoreline constraint generation, convolutional neural network residual correction to fusion output.

[0046] refer to Figure 2 Preferably, the spatial consistency module includes a raster reference determination submodule, a timeliness alignment submodule, and a channel construction submodule. The raster reference determination submodule uses the effective coastal waters corresponding to the hydrodynamic calculation grid as the target raster. Specifically, the target raster is not based on a general map grid, but on effective sea area grid points capable of supporting the water level output of the coupled model. For land area grid points, the raster reference determination submodule only retains their mask properties and does not generate residual output values. For nearshore narrow channels, bays, and estuaries, the raster reference determination submodule retains effective water area markers based on the water connectivity between adjacent grid points in the hydrodynamic grid, preventing incorrect connection of the shoreline by regular grids. After the target raster is determined, the system assigns a grid point index, a shoreline index, an effective sea area identifier, and a boundary transition identifier to each grid point.

[0047] The time-lead time alignment submodule registers the wind stress field, pressure field, forecast tide level, and astronomical tide components to the same timescale according to the forecast start time and forecast lead time. Meteorological fields are typically output at fixed forecast intervals, while the output interval of the hydrodynamic model and the tide level recording interval of the representative station may differ. The time-lead time alignment submodule uses the tide level output lead time of the coupled model as the target lead time and selects adjacent meteorological fields or astronomical tide components before and after the target lead time for time registration. When the source data exactly covers the target lead time, the corresponding value is used directly. When the source data is located on both sides of the target lead time, weights are formed according to time distance. When source data is missing, a missing data flag is set for that channel, and the missing data flag is used as the input masking condition for subsequent convolutional neural networks. This processing ensures that different channels in the same target sample express the physical state of the same forecast lead time.

[0048] The channel construction submodule encodes the historical tidal residuals under the same tidal phase, the current forecast lead time number, and the water depth gradient as additional channels, which, together with the forecast tidal level, form the input samples for the convolutional neural network. The historical tidal phase residuals are not simply the most recent residuals; instead, segments similar to the current tidal phase are found during historical storm events or regular tidal events, and the difference between the measured tidal level and the forecast tidal level of the coupled model is extracted as the residual prior. The forecast lead time number is used to distinguish the differences in error accumulation patterns between short-lead and long-lead forecasts. The water depth gradient encoding is used to indicate the location of abrupt changes in nearshore water depth in the network, preventing the convolutional network from treating the residuals in deep water areas and shallow water areas as the same texture. The channel-constructed samples are input into the network in the form of three-dimensional tensors, with the tensor dimensions corresponding to spatial grid points, forecast lead time, and physical channels. This embodiment uses the above processing to ensure that the input samples have the same reference benchmark in both space and time.

[0049] refer to Figure 3 In a preferred embodiment, the shoreline constraint generation module includes a water-land masking encoding submodule, a shoreline distance encoding submodule, and a convolutional neighborhood filtering submodule. The water-land masking encoding submodule divides the coastal grid into effective sea area grid points, land area grid points, and boundary transition grid points. Effective sea area grid points are those that can output tidal residual corrections; land area grid points do not participate in residual output; and boundary transition grid points are used to indicate to the convolutional neural network that both sea and land areas may exist in its neighborhood. For boundary transition grid points, the water-land masking encoding submodule does not simply delete them but retains their boundary attributes, enabling the network to distinguish between continuous offshore areas and nearshore constrained areas. Land area grid points are assigned a label indicating they cannot participate in feature aggregation, and missing test grid points are assigned an input masking label for the training and inference phases.

[0050] The shoreline distance encoding submodule calculates the normalized distance from each valid sea area grid point to the nearest land-water boundary along the coastal direction, and combines this with the location of abrupt changes in water depth to form a boundary-sensitive code. The calculation of the normalized distance is limited to the connected range of the real sea area; straight-line crossings of land to find the shoreline are not allowed. When the bay interior and open sea areas are close in regular distances but the waters are not connected, the shoreline distance encoding submodule uses the connected path as the calculation path. The location of abrupt changes in water depth can be obtained from the water depth difference between the target grid point and its adjacent valid sea area grid points; the greater the water depth difference, the higher the boundary-sensitive code. The boundary-sensitive code is used to instruct the convolutional network to maintain stronger constraints on residual gradient changes at that location, rather than applying a uniform treatment to all nearshore areas.

[0051] In practical implementation, the shoreline constraint strength can be calculated using the following formula:

[0052]

[0053] in, Representing grid points The strength of shoreline constraints; Representing grid points The effective sea area mask is set to 1 for sea area grid points and 0 for land area grid points. Representing grid points Normalized distance from the coastal connectivity path to the nearest land-water boundary; Representing grid points The magnitude of the water depth gradient at that location; and This indicates the weights of the shoreline distance term and the water depth variation term; and This represents the normalized scale parameter; the exponential operation describes the relationship where the constraint strength is higher when close to the shoreline, and the fractional operation is used to convert the water depth gradient into a bounded constraint. The physical meaning of this formula is that grid points in sea areas close to the shoreline and with large water depth variations should be subject to stronger boundary constraints in residual learning. For example, a grid point in a certain sea area has an effective sea area mask of 1, a normalized shoreline distance of 0.2, and a water depth gradient magnitude of 4. Take 0.6, Take 0.4, Take 1, Taking a value of 2, the shoreline constraint strength is approximately 0.758; if the same location is a land grid point, Setting it to 0 results in a calculation result of 0, indicating that the grid point does not participate in the effective sea area residual output.

[0054] The convolutional neighborhood selection submodule masks and reweights the convolutional sampling neighborhoods of the convolutional neural network based on land-water masking and boundary-sensitive coding. Specifically, for candidate convolutional neighborhoods of the target grid point, the submodule determines one by one whether the candidate neighborhood grid point is a valid sea area, whether it is connected to the target grid point's water area, whether it is a missing grid point, and whether it crosses a land-water boundary. When a candidate neighborhood grid point is a land area grid point, its neighborhood contribution is set to 0; when a candidate neighborhood grid point is adjacent to the target grid point on a regular grid but the water areas are not connected, its neighborhood contribution is set to 0; when a candidate neighborhood grid point is a boundary transition grid point, its contribution is attenuated according to the shoreline constraint strength. Table 2 shows the processing method of shoreline constraint coding in convolutional neighborhood selection. In this embodiment, convolutional constraint information is generated jointly by land-water masking, shoreline distance, and water depth gradient, so that the network follows the actual near-shore water boundary during the feature aggregation stage.

[0055] Table 2. Shoreline Constraint Encoding and Convolutional Neighborhood Processing

[0056]

[0057] Furthermore, the residual correction module includes a shared feature extraction submodule, a multi-scale residual branch, and a shoreline-constrained convolution branch. The shared feature extraction submodule receives multi-time, multi-channel samples and combines wind stress, air pressure, forecast tide level, astronomical tide, and historical residuals for each grid point in adjacent forecast lead times into basic spatiotemporal features. The shared feature extraction submodule can employ a structure combining temporal and spatial convolution. Temporal convolution extracts the error evolution relationship along the forecast lead time direction, while spatial convolution extracts the storm surge distribution relationship along the effective sea area grid points. The feature tensor formed after shared feature extraction is passed to multiple residual branches to distinguish error sources at different scales.

[0058] The multi-scale residual branch extracts residual features corresponding to typhoon-scale external forces, nearshore local water level rise, and tidal phase differences using convolutional kernels with different receptive fields. Branches with larger receptive fields absorb the background water level rise caused by large-scale wind stress and pressure fields, while branches with smaller receptive fields describe local error variations in bays, estuaries, and narrow channels. Tidal phase features are input into the network through additional channels, ensuring that residuals corresponding to different tidal phases under the same external force condition are not confused. The outputs of multiple residual branches are fused along the channel dimension, and the output layer generates a residual correction with the same resolution as the predicted tide level. The shoreline-constrained convolutional branch embeds convolutional constraint information during the calculation of convolutional kernel weights, ensuring that convolutional sampling is not unconditionally performed within a fixed rectangular window but is constrained by land-water masking, water connectivity, and boundary-sensitive encoding.

[0059] The shoreline-constrained convolution branch can be expressed using the following constrained convolution expression:

[0060]

[0061] in, Indicates the first In-layer grid points and feature channels The output characteristics; Representing grid points The candidate convolutional neighborhood; Indicates the first Relative position in the layer and channels The corresponding convolutional kernel weights; Representing grid points With neighboring grid points The shoreline constraint neighborhood coefficient between them is 0 for land areas or disconnected neighborhoods, and non-zero values ​​are taken for connected sea areas according to the boundary sensitive coding. Indicates the first In-layer neighborhood grid points Input features; Indicates the bias term; This represents a nonlinear mapping operation. The physical meaning of this formula is that the convolutional features are provided by the neighborhood of the propagating water area, rather than by all the grid points within a normal rectangular window. For example, if a target grid point has three candidate neighborhood points with eigenvalues ​​of 0.4, 0.5, and 0.8, corresponding to a convolutional kernel weight of 0.6, shoreline constraint neighborhood coefficients of 1, 0, and 0.5, and a bias term of 0, then the weighted result before nonlinear mapping is 0.48. The second neighborhood grid point, although within the regular window, is not included in the calculation because it is not connected.

[0062] In this embodiment, the tide level residual correction output by the residual correction module shares the same spatial grid point and the same forecast lead time index as the predicted tide level. The fusion output module includes a residual confidence assessment submodule, an anomaly correction constraint submodule, and a result synthesis submodule. The residual confidence assessment submodule generates confidence weights based on the spatial continuity of the residuals output by the convolutional neural network, the similarity of historical errors along the same shoreline, and the completeness of the input samples. The spatial continuity of the residuals can be determined by the residual difference between the target grid point and neighboring connected grid points; the similarity of historical errors along the same shoreline can be determined by the distance between the current residual pattern and the residual patterns under similar historical tidal phases; the completeness of the input samples can be determined by the missing measurement markers and masking ratios of each channel. The anomaly correction constraint submodule limits the magnitude of the tide level residual correction at low confidence weight grid points and corrects the residuals at the shoreline boundary transition grid points using the consistency verification results of adjacent effective sea area grid points. The result synthesis submodule superimposes the constrained tide level residual correction onto the predicted tide level to form grid point prediction values, and can generate representative station prediction values ​​through the mapping relationship between representative stations and surrounding effective grid points.

[0063] The fused output can be executed according to the following formula:

[0064]

[0065] in, Representing grid points Storm surge forecast water level after fusion; This indicates that the coupled model is at the grid. Forecast tide level at the location; This represents the residual confidence weight, and its value is determined by the input completeness, spatial continuity, and historical error similarity. This represents the tidal residual correction amount after the output of the convolutional neural network has been constrained by anomaly correction. Addition represents the compensation of the residual correction amount for the coupled model's tidal level, and multiplication represents the constraint of the confidence weight on the residual correction amount. The physical meaning of this formula is that the final output is based on the coupled model's tidal level, only incorporating the residual correction controlled by the confidence level. For example, if the coupled model predicts a tidal level of 2.4 meters for a certain grid point, the residual correction amount is 0.3 meters, and the residual confidence weight is 0.7, then the merged water level is 2.61 meters. If there are many missing measurements in the input of this grid point, leading to a decrease in the confidence weight, then the magnitude of the same residual correction amount participating in the synthesis will decrease synchronously. This embodiment ensures that the residual correction process maintains consistency with the input data quality and boundary continuity through confidence assessment, anomaly constraint, and result synthesis.

[0066] refer to Figure 4 In a preferred embodiment, the system further includes a sample construction module, which comprises an event slicing submodule, a phase matching submodule, and a residual label generation submodule. The event slicing submodule forms sample time windows based on the start time, maximum rise time, and receding time of historical storm events. Specifically, the samples from historical storm events are not arbitrarily selected on fixed dates, but rather sliced ​​around key water level change stages in the storm surge process. The start time corresponds to the initial forecast state, the maximum rise time corresponds to the peak storm surge response, and the receding time corresponds to the weakening stage of the rise. The event slicing submodule combines the forecast tide level, wind stress field, pressure field, astronomical tide component, and measured tide level records covered by the above stages into training samples, ensuring that the samples contain complete error evolution information from the establishment to the decay of the rise.

[0067] The phase matching submodule maps tide level sequences from different storm processes to training segments with consistent phases according to the astronomical tide phase. Since the total water level error generated by a storm of the same intensity at high tide, low tide, or during the tidal transition phase has different expressions, matching cannot be based solely on real-time time or the time difference from the maximum water level rise during sample construction. The phase matching submodule extracts the astronomical tide phase of each training segment, grouping segments with similar phases and forecast lead times into the same training neighborhood for constructing historical tidal phase residual channels. The residual label generation submodule constructs residual labels using the difference between the measured tide level and the forecast tide level, and sets training masking markers for land-water boundaries, missing measurement times, and abnormal observation times. When there are short-term missing measurements or abnormal jumps in the measured tide level, the residual label generation submodule does not use that time as the supervision target, but only retains its input missing measurement marker to prevent outliers from directly entering residual learning.

[0068] The phase matching distance can be determined using the following formula:

[0069]

[0070] in, Represents sample fragments With sample fragments Phase matching distance between them; and These represent the astronomical tidal phases of the two sample segments respectively; and These represent the forecast lead times for the two sample segments, respectively. The weights of the cosine phase difference term are indicated. This indicates the weight of the forecast lead time difference term; absolute value operations are used to measure the magnitude of the difference, and sine and cosine operations are used to handle the periodicity of tidal phases. The physical meaning of this formula is that historical segments with similar tidal phases and forecast lead times are more suitable as residual references for the current sample. For example, sample segments... The phase is 1.2 radians, sample fragment The phase is 1.0 radians, and the forecast lead times are 6 and 7 respectively. Take 0.3, Taking 0.05, the phase matching distance is approximately 0.302; this value is smaller than that of segments with larger phase differences, indicating that the segment... It is more suitable for participating in the construction of historical tidal phase residual channels.

[0071] The training labels generated by the residual label generation submodule and the residual correction values ​​output by the convolutional neural network use the same grid index and time index. When the representative station is located outside the target coastal grid, the system assigns the residual label corresponding to the measured tide level of the station to the relevant grid points through the spatial mapping relationship between the station and the surrounding effective sea area grid points; when a grid point is affected by multiple stations, the weights are formed by station distance, shoreline consistency, and water connectivity. For areas without station coverage, the system does not forcibly generate measured residual labels, but only retains the coupled model output and shoreline constraint information for inference processing. Table 3 shows the organization of training samples and labels. This embodiment uses event slicing, tidal phase matching, and residual label masking to enable the training samples to reflect the temporal changes and boundary availability during storm surge.

[0072] Table 3. Construction of Training Samples and Residual Labels

[0073]

[0074] In a preferred embodiment, the residual correction module further includes a graph convolutional adjacency correction submodule. The graph convolutional adjacency correction submodule constructs an effective sea area grid adjacency matrix based on shoreline connectivity, water depth similarity, and coastal propagation direction. Regular raster convolution determines the neighborhood with a fixed window, making it impossible to distinguish whether the neighborhood within the rectangular window is separated by land. The graph convolutional adjacency correction submodule treats each effective sea area grid point as a node, the real water connectivity between two grid points as an edge, and adjusts the edge weights according to the coastal propagation direction and water depth similarity. When the regular raster convolution window crosses land or isolated water areas, the graph convolutional adjacency correction submodule replaces cross-land adjacency edges with adjacency edges along the real water connectivity path, enabling residual features to propagate along the bay interior, estuary channel, or continuous shoreline direction.

[0075] In practical implementation, water connectivity can be determined by land-water shielding. If two grid points are adjacent on a regular grid and there is no land shield between them, a candidate connectivity edge is established; if two grid points are adjacent on a regular grid separated by land, no connectivity edge is established; if two grid points are connected by a curved waterway, although the straight-line distance is large, the length along the water path is within the adjacency range, then an adjacency edge along the water path can be established. Water depth similarity is used to limit the residual propagation intensity between abrupt changes in deep and shallow water regions, and the coastal propagation direction is used to describe the main direction of storm surge residual propagation along the coast. The constructed adjacency matrix serves as an additional input to the shoreline-constrained convolutional branch. The convolutional neural network performs gating fusion between regular convolutional features and graph adjacency features, and the gating coefficients are jointly determined by boundary-sensitive coding, adjacency edge weights, and input completeness.

[0076] The adjacency weights of graph convolution can be calculated using the following formula:

[0077]

[0078] in, Represents the effective sea area grid. With grid points Connectivity adjacency weights between them; This indicates whether there is a real waterway connecting the two; it is set to 1 if it exists and 0 if it does not. This represents the normalized distance between the two along their actual waterway paths; and These represent the water depth at two grid points respectively; and Scale parameters representing distance decay and water depth difference decay; This represents the consistency coefficient of propagation direction along the shore; the exponential operation is used to convert path distance and water depth difference into continuously decaying terms, and the multiplication operation indicates that the adjacent weight decreases when any key constraint is missing. The physical meaning of this formula is that grid points that are actually connected in the water, have short paths, similar water depths, and consistent propagation directions have higher weights in the propagation of graph convolution residuals. For example, if two grid points are actually connected, the normalized path distance is 0.3, and the water depth difference is 2, Take 1, If we take a value of 4, the consistency coefficient of propagation direction is 0.8, then the adjacency weight is approximately 0.359; if the two are separated by land, If the adjacency weight is 0, the adjacency weight is directly 0.

[0079] In this embodiment, the fusion of regular convolutional features and graph adjacency features can be accomplished by a gating layer. The gating layer receives the boundary-sensitive encoding of the target grid points, the mean adjacency weights, the input missing detection ratio, and the shared feature vector, and outputs a gating value between 0 and 1. When the gating value is high, graph adjacency features account for a higher proportion in the residual representation; when the gating value is low, regular convolutional features account for a higher proportion. For continuous offshore areas, the regular convolutional window is close to the connectivity of the real waters, and the gating value can be biased towards regular convolutional features; for the inner side of bays, areas with curved coastlines, or narrow waterways, graph adjacency features can replace cross-land convolutional adjacency. This embodiment transforms the regular grid spatial relationship into a residual feature propagation relationship that conforms to the connectivity of nearshore waters through graph convolutional adjacency correction.

[0080] Furthermore, the system also includes a physically consistent training module, which comprises a marine continuity constraint submodule, a boundary shielding constraint submodule, and a residual gradient constraint submodule. The marine continuity constraint submodule smooths the residual changes of adjacent valid marine grid points, but the smoothing range is limited to grid points connected to real water areas, not crossing land areas or non-propagating water areas. The boundary shielding constraint submodule sets loss exclusion markers for land area grid points, missing measurement grid points, and non-propagating water area grid points, preventing these grid points from being used as sources of supervision error. The residual gradient constraint submodule determines the residual gradient penalty weights for different regions based on water depth gradient, shoreline distance, and historical extreme water increase distributions, thus subjecting the network's residual changes in complex nearshore areas to topographic and boundary-related constraints.

[0081] In specific training, the objective function of the convolutional neural network includes not only residual numerical error, but also residual spatial variation constraints and boundary availability constraints. Residual numerical error is used to make the network output approximate the residual labels constructed from measured tide levels; spatial variation constraints are used to ensure that the residual variation between adjacent connected sea area grid points is consistent with the residual variation in historical labels; boundary constraints are used to limit anomalous residual amplitudes near the shoreline where water depth changes abruptly. Grid points in the training samples labeled as missing, anomalous, or land-based are not included in the supervised loss to prevent the network from learning data gap patterns unrelated to actual water levels.

[0082] The physical consistency training objective can be expressed by the following formula:

[0083]

[0084] in, This represents the training objective of the convolutional neural network; This represents the set of coastal grid points involved in the training; The training effectiveness mask is generated jointly by effective sea area markers, missing measurement markers, and anomaly observation markers. Representing grid points The network output residual; Representing grid points The residual label; Representation and lattice The set of adjacent grid points connected by real water bodies; Representing grid points With grid points The connected adjacency weight; Representing grid points The strength of shoreline constraints; , and These represent the weights of the residual numerical term, the residual spatial variation term, and the boundary magnitude term, respectively. The squaring operation penalizes deviations in the residual value and residual gradient, while the absolute value operation limits excessively large residual outputs in the boundary region. The physical meaning of this formula lies in incorporating the residual numerical value, residual propagation continuity, and shoreline boundary constraints into the same training process. For example, if the output residual of a grid point is 0.25 meters, the residual label is 0.20 meters, the difference between the output residuals and the label difference of adjacent grid points is 0.04 meters, and the shoreline constraint strength is 0.7, when the weights take commonly used normalized values, the training loss of this grid point is composed of the numerical error, the adjacency variation error, and the boundary magnitude constraint, rather than being determined solely by a single-point error of 0.05 meters.

[0085] Table 4 shows the input sources and processing boundaries of different constraints in physical consistency training. This table illustrates the correspondence between the training objective and the aforementioned shoreline constraints, graph adjacency, and residual labels. During implementation, each constraint can be enabled or disabled based on sample completeness, without changing its technical meaning.

[0086] Table 4 Physical Consistency Training Constraints

[0087]

[0088] In this embodiment, the convolutional neural network (CNN) after training retains shared feature extraction parameters, multi-scale residual branch parameters, shoreline constraint convolution branch parameters, and graph adjacency fusion parameters. During the inference phase, the current coupled model output and current shoreline constraint information are input, and the network outputs residual corrections using the same data organization method as in the training phase. Because the training process excludes land areas, missing measurements, and non-propagating grid points, and introduces residual gradient constraints in the boundary regions, the residual field in the inference phase remains consistent with the physical boundary processing in the training phase. This embodiment, through physically consistent training, enables the CNN residual learning process to not rely on the implicit continuity assumption of ordinary image convolution, but instead uses nearshore water connectivity, shoreline boundaries, and water depth variations as training constraints.

[0089] refer to Figure 5 In a preferred embodiment, the system further includes an online drift calibration module. The online drift calibration module includes a zonal residual monitoring submodule, an input distribution comparison submodule, and a local parameter update submodule. The zonal residual monitoring submodule statistically analyzes the consistency of residual directions within consecutive forecast periods according to shoreline zoning. Shoreline zoning can be formed based on tidal characteristics, water depth changes, historical error correlations, and shoreline connectivity. Each zoning contains several effective sea area grid points and several representative stations. During operation, when measured tide levels or validated residual feedback are available, the zonal residual monitoring submodule calculates the forecast residual directions for multiple consecutive forecast periods within the same shoreline. If the residuals are consistently positive, it indicates that the coupled model may be continuously underestimating the water level in that shoreline; if the residuals are consistently negative, it indicates that the coupled model may be continuously overestimating the water level in that shoreline; if the residual directions change frequently, local updates are not triggered.

[0090] The input distribution comparison submodule calculates the distance between the feature distributions corresponding to the current wind field, pressure field, tidal phase, and water depth gradient and the feature distributions in the training sample library. The current storm process may differ from historical training samples in terms of path, wind field structure, tidal phase combination, or nearshore response. Relying solely on the residual direction may misjudge observation noise as model drift. Therefore, the input distribution comparison submodule encodes the statistical features of the current input sample and compares them with the feature distributions of the same or similar shore segments in the historical sample library. When both residual direction consistency and feature distribution distance meet the triggering conditions, the local parameter update submodule only updates the local branch parameters of the convolutional neural network for the corresponding shore segment, while keeping the shared feature extraction parameters frozen. Freezing the shared feature extraction parameters preserves the learned general spatiotemporal features from historical samples, while updating the local branch parameters adapts to the error drift of the current shore segment.

[0091] Online drift rating can be calculated using the following formula:

[0092]

[0093] in, Indicates shoreline zoning Drift rating; Indicates partition The number of forecast lead times for internal monitoring; Indicates partition The monitoring timeframe set; Indicates partition Timeliness The average forecast residuals under the following conditions; The sign function is used to extract the residual direction. Indicates the current input features Features of historical sample database The distribution distance between them; Indicates partition The average residual confidence weight; , and This represents the weights of residual direction consistency, input distribution distance, and insufficient confidence terms. The physical meaning of this formula is that drift triggering depends not only on a single error but also on the direction of continuous errors, the difference between the input sample and historical samples, and the residual confidence state. For example, in a certain shoreline segment, the residuals are positive in 4 out of 5 timeframes and negative in 1 timeframe, with a sign mean absolute value of 0.6, a feature distribution distance of 0.4, and an average confidence weight of 0.75. , , If the values ​​are 0.5, 0.3, and 0.2 respectively, the drift score is 0.47. When the preset trigger condition is higher than this value, no local update is performed. When the trigger condition is lower than this value and other verification conditions are met, only the local branch parameters of the corresponding shore segment are updated.

[0094] When performing updates, the local parameter update submodule sets the local branch parameters of the corresponding shore segment to a trainable state and freezes the shared feature extraction layer, multi-scale basic branches, and shoreline constraint generation logic. After the current sample enters the network, only the local parameter layers related to that shore segment are adjusted through backpropagation. The updated samples include currently available measured residual labels and highly reliable pseudo-labels obtained through pseudo-supervision screening (described later). To avoid local parameters being completely swayed by a single storm process, the online drift calibration module limits the shore segment range, tidal phase range, and time range of the sample source in each update, and recalculates the partitioned residual scores after the update. If the consistency of the residual direction decreases after the update and the input distribution distance remains within an acceptable range, the updated parameters are retained; if the continuity of residuals between adjacent shore segments is disrupted after the update, the updated parameters are rolled back. This embodiment, through partitioned monitoring, distribution comparison, and local parameter updates, enables the convolutional neural network to have controlled calibration capabilities during continuous operational use.

[0095] Furthermore, the online drift calibration module also includes a replay constraint submodule and a pseudo-supervision screening submodule. The replay constraint submodule selects sample segments from the historical storm sample library that match the current shoreline, tidal phase, and wind field direction, and these segments participate in the local parameter update together with the current samples. The selection of replay samples is not random sampling, but is determined based on shoreline index, phase matching distance, wind field direction similarity, and input completeness. If the current shoreline is located inside the bay, segments with similar shoreline constraint strength and water connectivity structure from historical samples are selected first; if the current process is in the recession phase, historical segments from the recession phase are selected first. The replay constraint submodule retains the residual supervision of historical samples during local parameter updates, ensuring that the new sample update does not overwrite the residual expressions of typical historical storm processes.

[0096] When a representative tide level station lacks measured data, the pseudo-supervised screening submodule generates candidate pseudo-labels using the residuals of adjacent valid sea area grid points, the propagation delay of the same shore segment, and the consistency of residuals between different time periods. Specifically, when a representative station lacks measured tide levels in the current time period, but its adjacent valid sea area grid points have already generated residual feedback from other stations or high-confidence grid points, the pseudo-supervised screening submodule searches for candidate grid points along the actual water connectivity path and reads the residuals from the previous or next time period according to the propagation delay. After the candidate pseudo-labels are generated, they do not directly participate in training but are filtered based on the confidence weights, adjacency connectivity weights, and consistency between different time periods output by the residual confidence assessment submodule. Low-confidence candidate pseudo-labels are excluded, and high-confidence pseudo-supervised labels participate in local parameter updates together with the measured residual labels.

[0097] The pseudo-supervised residual labels can be generated using the following formula:

[0098]

[0099] in, Indicates the site Timeliness Candidate pseudo-supervised residual labels; Indicates and represents the site A set of adjacent valid sea area grid points within the same real water area connectivity range; Indicates neighboring grid points The residual confidence weights; Indicates the site With neighboring grid points The site mapping weights between them are determined by distance, shoreline consistency, and waterway connectivity; Indicates neighboring grid points After deducting the propagation delay The residuals after; This represents the denominator's stable term. The physical meaning of this formula is that the candidate residual labels for missing stations are formed by weighting the residuals of highly reliable neighboring grid points within the same water area's connectivity range, taking into account residual propagation delay. For example, a missing station corresponds to two neighboring grid points with residual confidence weights of 0.8 and 0.6, and station mapping weights of 0.9 and 0.7, respectively. The residuals after propagation delay are 0.2 meters and 0.4 meters, respectively. When the stable term takes a very small value, the candidate pseudo-supervision residual is approximately 0.274 meters. If the confidence weight of one of the grid points is lower than the screening criteria, that grid point will not participate in the pseudo-label construction.

[0100] In this embodiment, the pseudo-supervised screening submodule also performs temporal consistency verification on candidate pseudo-labels. If the direction of change of candidate residuals at the same station in adjacent time periods is opposite to the direction of change of residuals in the neighboring grid group, the candidate pseudo-label is marked as low confidence. If the candidate pseudo-label differs too much from the historical phase-matching residuals of the same shore segment, and the current input completeness is insufficient, the candidate pseudo-label will not participate in the local parameter update. The replay constraint submodule inputs historical samples, current measured residual labels, and high-confidence pseudo-supervised labels into the local parameter update process, limiting the update object to the local branch parameters of the corresponding shore segment. After the update is completed, the system re-executes the fusion output, and the grid point confidence weights are updated by the residual confidence assessment submodule. This embodiment, through historical sample replay and pseudo-supervised screening, ensures that online drift calibration still has a controlled data source under conditions of incomplete observations and avoids low-confidence pseudo-labels from changing the shared residual expression.

[0101] In a preferred embodiment, the representative station forecast value is obtained by mapping the grid forecast value. The system establishes a mapping relationship between the representative station and adjacent valid sea area grid points on the target coastal grid. The mapping relationship is not determined solely by straight-line distance, but simultaneously considers the shoreline segment to which the station belongs, the water connectivity path, and the shoreline constraint strength. When the representative station is located inside a estuary or bay, even if the offshore grid points are close in straight line, they will not participate in the station value synthesis in the case of non-connectivity or cross-land areas; if the grid points in the same waterway are continuous along the water path, they can participate in the synthesis according to the station mapping weight. The generation of the station forecast value adopts the grid forecast water level in the fusion output module to avoid the use of different residual sources for the station results and the area results. For the case where the station's measured feedback enters online drift calibration, the system reverse maps the station residual to its adjacent valid sea area grid points, but the mapping process is still constrained by water connectivity and confidence weights.

[0102] In this embodiment, shoreline partitioning can be formed before model training or re-validated during sample database updates. The basic criteria for shoreline partitioning include similarity of astronomical tidal phase responses, correlation of historical forecast residuals, shoreline connectivity, and continuity of water depth gradients. Adjacent grid points are assigned to the same shoreline partition if their residual changes in the same direction during historical storms, their tidal phase responses are similar, and their waterways are connected; otherwise, they are assigned to different partitions if they are separated by land or if abrupt changes in water depth cause differences in residual propagation relationships. The partitioning results are used for residual monitoring, local parameter updates, and representative station mapping. During online calibration, the system only allows adjustments to local branch parameters within the corresponding partition, without changing the parameter states of other partitions. Through this partitioning mechanism, local drift will not extend unconstrainedly along regular grids to unrelated shorelines.

[0103] Furthermore, the completeness of the input sample can be generated jointly by the validity identifiers of each channel. For a multi-channel input at a certain time point, if the forecast tide level, wind stress field, pressure field, and astronomical tide component are all available, and the historical residual channels with the same tidal phase have a phase reference, then the input completeness is high; if the meteorological field lacks a certain time point or the historical residual channels have no phase-matching samples, then the input completeness is reduced. The residual confidence assessment submodule synthesizes the input completeness with the residual spatial continuity and historical error similarity into a confidence weight. The anomaly correction constraint submodule sets a residual amplitude constraint for low-confidence grid points. This constraint is not uniformly processed with a fixed global threshold, but is determined by combining the shoreline constraint strength, the residuals of adjacent connected grid points, and the current forecast time point. In areas with high shoreline constraint strength and large differences in residuals among neighboring grid points, the system adopts a more conservative composite weight for the residual correction amount.

[0104] In this embodiment, the training and inference of the convolutional neural network maintain the same data interface. During training, the input includes the historical coupled model output, multi-channel samples, shoreline constraint information, graph adjacency matrix, and residual labels. During inference, the input includes the current coupled model output, multi-channel samples, shoreline constraint information, and graph adjacency matrix; residual labels are not included in the inference process. The residual correction module learned during training outputs the residual field, and the current residual correction is generated using the same output structure during inference. The physically consistent training module only participates in parameter updates during training or online calibration, but the boundary shielding, connectivity adjacency, and residual gradient constraints it forms are still reflected in the inference stage through the shoreline constraint generation module and the graph convolutional adjacency correction submodule. Therefore, the system will not exhibit a situation where shoreline constraints are used during training but degenerate into ordinary regular convolution during inference.

[0105] In one embodiment, when a storm process enters the nowcasting phase, the system reads the output of the coupled model at the current forecast start time and forms current multi-time, multi-channel samples through the spatial consistency module. The shoreline constraint generation module calls existing land-water masks, water depth gradients, and water connectivity relationships to generate convolutional constraint information for the current grid points. The residual correction module inputs the current samples into the convolutional neural network and outputs the tide level residual correction for each effective sea area grid point. The fusion output module generates confidence weights based on the completeness of the input samples, the spatial continuity of the residuals, and the similarity of historical errors, and superimposes the constrained residuals onto the tide level predicted by the coupled model. If there is already measured feedback from some representative stations in the current forecast period, the online drift calibration module determines whether the feedback meets the conditions of zonal residual direction consistency and input distribution distance; if the conditions are met, only the local branch parameters of the corresponding shore segment are updated, and the residual correction for the shore segment in subsequent forecast periods is regenerated after the update. This process establishes a closed relationship between the data flow, residual learning, and online calibration in the nowcasting phase.

[0106] In another optional embodiment, the system can periodically reorganize the historical sample library. The sample library reorganization process includes deleting residual labels marked as anomalous observations, adding new storm process slices, updating the phase matching index within the shoreline partitions, and recalculating the input distribution characteristics of historical samples. For newly added historical storm processes, the event slice submodule forms sample time windows according to the reporting, maximum rise, and recession stages; the phase matching submodule calculates the phase matching distance between this process and existing samples; and the residual label generation submodule writes the difference between the measured tide level and the predicted tide level from the coupled model into the residual label library. If the new sample involves shoreline redrawing or water depth data updates, the shoreline constraint generation module regenerates the corresponding land-water mask and water depth gradient codes to avoid mixing old and new shoreline constraints. After the sample library is updated, the physical consistency training module can perform batch training on the convolutional neural network or calibrate training on local branches.

[0107] Furthermore, the system maintains consistency between input masking and training masking when processing missing data. For missing meteorological field data, the spatial consistency module does not directly fill in the missing channel values, but instead sets a missing channel marker and retains this marker in the input of the convolutional neural network, enabling the network to identify that the channel is unavailable. For missing measured tide levels, the residual label generation submodule does not generate supervised labels; if online calibration is required, the pseudo-supervised screening submodule must pass neighbor grid confidence weights, station mapping weights, and temporal consistency checks before generating candidate pseudo-labels. For land areas or non-propagating water areas, the boundary masking constraint submodule excludes corresponding grid points in the training loss, and the convolutional neighborhood screening submodule excludes corresponding neighborhoods in the inference convolution. This processing prevents missing data and land area grid points from participating in residual feature learning in the form of implicitly filled values.

[0108] In this embodiment, the system can save the input sample index, shoreline constraint code, residual correction amount, residual confidence weight, and fused water level for each forecast result. Saving these intermediate results is used to track the forecast result formation process without changing the model output logic. If a local abrupt change occurs in the forecast result for a certain grid point, the system can backtrack the convolutional neighborhood coefficients, graph adjacency weights, and input completeness of that grid point to determine whether the abrupt change originates from the coupled model's forecast tide level, the convolutional residual output, or the fusion confidence constraint. For representative station results, the system saves the station mapping grid points and mapping weights, ensuring a verifiable relationship between the station forecast values ​​and the area grid point forecast values. This embodiment, by uniformly recording intermediate quantities, provides a clear data chain for the residual correction process of the storm surge forecast system.

[0109] In one embodiment, the convolutional neural network can consist of temporal convolutional layers, spatial convolutional layers, shoreline-constrained convolutional layers, multi-scale residual fusion layers, and residual output layers. The temporal convolutional layers extract the temporal relationships between wind stress, air pressure, astronomical tides, and predicted tide levels along the forecast lead time; the spatial convolutional layers extract the water level distribution relationships along the effective sea area grid; the shoreline-constrained convolutional layers perform constrained convolutions based on the neighborhood coefficients output by the neighborhood selection submodule; the multi-scale residual fusion layer receives features from different receptive field branches and forms unified residual features; the residual output layer maps the residual features to tide level residual corrections. During network training, the supervision target of the residual output layer is the residual label after subtracting the predicted tide level from the measured tide level. During network inference, the residual corrections generated by the residual output layer are synthesized into the final predicted water level by the fusion output module. This network structure centers on residual learning, avoiding the use of convolutional neural networks as a substitute model for the complete storm surge dynamic process.

[0110] Preferably, in the early stages of training, the neighborhood coefficient generation logic in the shoreline constraint convolution branch can be frozen first, and only the shared feature extraction submodule and the multi-scale residual branch are trained, allowing the network to form a basic residual representation. Subsequently, graph convolutional adjacency correction and physical consistency training are enabled, allowing the network to gradually accept water connectivity and boundary constraints. This training arrangement does not change the system structure, but only controls the parameter update range. For shorelines with a small number of samples, the basic feature extraction parameters of neighboring similar shorelines can be shared, and only the local branch parameters of this shoreline segment are trained. For shorelines with a large number of samples, the local parameters in the multi-scale residual branch can be trained simultaneously, but the shoreline constraint generation logic is still determined by the land-water mask and water depth gradient, and is not freely learned by the network. This treatment prevents the network from treating the shoreline boundary as ordinary texture features and performing unconstrained fitting.

[0111] In a preferred embodiment, the anomaly correction constraint submodule performs a consistency check on the residual correction amount based on connected neighborhoods. The system takes the set of real-water adjacent grid points of the target grid point and calculates the median trend and range of variation of the residual correction amounts of adjacent grid points. When the residual correction amount of the target grid point deviates from the overall trend of the connected neighborhoods, and the input integrity of the target grid point is lower than a preset condition, the anomaly correction constraint submodule reduces the confidence weight of that grid point. If the target grid point is located in a region of abrupt changes in water depth, the system does not require it to be completely smooth with the residuals of adjacent grid points, but relaxes or tightens the constraint range according to the water depth gradient and the shoreline constraint strength. This processing preserves the residual gradient changes that may exist at locations such as estuaries and bay entrances, while preventing isolated anomaly residuals caused by low-quality inputs. The constrained residual correction amount enters the result synthesis submodule and forms the final water level with the tide level predicted by the coupled model.

[0112] Furthermore, when outputting storm surge forecast results, the system can simultaneously output grid point forecast values, representative station forecast values, residual corrections, and residual confidence weights. Grid point forecast values ​​are directly generated from the effective coastal grid; representative station forecast values ​​are synthesized from station mapping relationships; residual corrections reflect the compensation of the convolutional neural network for the coupled model forecast; and residual confidence weights reflect the degree of participation of this compensation in the fusion process. All of the above outputs originate from the same data processing flow and are not simply superimposed from ordinary display functions. The forecast values, residual values, and confidence weights maintain a computable relationship, facilitating the subsequent online drift calibration module's determination of whether a certain coastal segment exhibits persistent deviation. This output method allows residual correction and model calibration to share the same result structure.

[0113] In this embodiment, a defined data dependency relationship is formed between the various modules of the system. The coupled forecast input module provides the original forecast and historical residual sources; the spatial consistency module maps data from different sources to the same coastal raster sample; the shoreline constraint generation module converts land-water boundaries, water depth changes, and water connectivity into convolutional constraint information; the residual correction module outputs residual correction values ​​based on a convolutional neural network; the fusion output module forms the final water level based on confidence weights; the sample construction module and the physical consistency training module provide residual labels and constraint targets for network training; and the online drift calibration module performs controlled updates of local branch parameters based on residual feedback during the runtime phase. Each module addresses the technical problem that nearshore regular raster convolution cannot express shoreline boundaries and water connectivity constraints, and data flows between modules according to a unified grid, unified timeliness, and unified validity identifier.

Claims

1. A storm surge forecasting method based on a coupled model, characterized in that, Includes the following steps: Step S1: Obtain the forecast tide level, wind stress field, pressure field, astronomical tide component, and historical tide level residuals under the same tidal phase from the storm surge numerical coupling model, and establish a unified data index and validity identifier. Step S2: Map the predicted tide level, wind stress field, air pressure field, historical tide level residuals under the same tidal phase, and astronomical tide components to the same effective coastal sea area grid to construct multi-time multi-channel samples. Step S3: Generate constraint information for convolution calculation based on shoreline mask, distance between land and water boundaries, and water depth changes; Step S4: Input the multi-time multi-channel samples and the constraint information generated in step S3 for convolution calculation into the convolutional neural network, perform shoreline constraint residual learning, and output the tide level residual correction amount with the same spatial resolution and time index as the predicted tide level. Step S5: Generate residual confidence weights based on the completeness of the input samples, the continuity of the residual space, and the similarity of historical errors on the same shore. After anomaly correction constraints are applied to the tide level residual correction, the weights are superimposed on the tide level forecast of the coupled model to generate storm surge forecast results.

2. The storm surge forecasting method based on a coupled model according to claim 1, characterized in that, Step S2 specifically includes: using the effective coastal sea area corresponding to the hydrodynamic calculation grid as the target grid, retaining the water area validity markers and assigning index identifiers to each target grid point; registering the wind stress field, air pressure field, forecast tide level and astronomical tide components to the same time scale according to the forecast start time and forecast lead time; encoding the historical tide level residuals under the same tidal phase, the current forecast lead time number and water depth gradient as additional channels, which together with the forecast tide level constitute the input tensor of the convolutional neural network.

3. The storm surge forecasting method based on a coupled model according to claim 2, characterized in that, Step S3 specifically includes: dividing the coastal grid into effective sea area grid points, land area grid points, boundary transition grid points, and missing measurement grid points, and generating a water-land mask code; calculating the normalized distance from each effective sea area grid point to the nearest water-land boundary along the real sea area connectivity path, and generating a boundary sensitive code based on the location of abrupt changes in water depth; and based on the water-land mask code and the boundary sensitive code, masking and reweighting the convolution sampling neighborhood so that land area grid points and missing measurement grid points do not participate in the residual feature aggregation of effective sea area grid points.

4. The storm surge forecasting method based on a coupled model according to claim 3, characterized in that, In step S4, shoreline constraint residual learning specifically includes: performing spatiotemporal joint encoding on multi-time and multi-channel samples to extract shared basic features; using convolutional kernels with different receptive fields to extract residual features corresponding to typhoon-scale external forces, nearshore local water level increases, and tidal phase differences; embedding convolution constraint information into the convolutional kernel weight calculation process, setting the feature responses corresponding to land grid points and missing grid points as non-participating quantities, and finally generating tidal level residual correction quantities.

5. The storm surge forecasting method based on a coupled model according to claim 4, characterized in that, Step S5 specifically includes: calculating residual confidence weights based on the spatial continuity of the residuals output by the convolutional neural network, the similarity of historical errors in the same shore segment, and the completeness of the input samples; limiting the magnitude of the tide level residual correction at low confidence weight grid points, and correcting the residuals at the shoreline boundary transition grid points using the consistency verification results of adjacent effective sea area grid points; and superimposing the limited tide level residual corrections onto the forecast tide level to generate a storm surge forecast result containing grid point forecast values ​​and representative station forecast values.

6. The storm surge forecasting method based on a coupled model according to claim 5, characterized in that, The training sample construction steps of the convolutional neural network include: forming sample time windows based on the start time, maximum water level rise time, and water level fall time of historical storm processes; mapping the tide level sequences of different storm processes to training segments with consistent phases according to the astronomical tide phase; constructing residual labels based on the difference between the measured tide level and the predicted tide level; and setting training masking marks for the land-water boundary, missing measurement time, and abnormal observation time.

7. The storm surge forecasting method based on a coupled model according to claim 6, characterized in that, Step S4 also includes a graph convolutional adjacency correction step: constructing an effective sea area grid adjacency matrix based on shoreline connectivity, water depth similarity, and coastal propagation direction; when the regular grid convolutional window crosses land or isolated water areas, replacing cross-land adjacency edges with adjacency edges along the actual water area connectivity path; and performing gating fusion between the regular convolutional features and the graph adjacency features to form a residual feature representation that conforms to the connectivity of nearshore waters.

8. The storm surge forecasting method based on a coupled model according to claim 7, characterized in that, The training of the convolutional neural network adopts physical consistency constraints, specifically including: smoothing constraints on the residual changes of adjacent valid sea area grid points; setting loss exclusion markers for land area grid points, missing grid points and non-propagable water area grid points; and determining the residual gradient penalty weights for different regions based on water depth gradient, shoreline distance and historical extreme water increase distribution, so that the training objective simultaneously constrains residual values, residual spatial changes and boundary validity.

9. The storm surge forecasting method based on a coupled model according to claim 8, characterized in that, Following step S5, an online drift calibration step is also included: based on the consistency of residual direction within the continuous forecast period according to the shore segment zoning statistics, the distance between the current input feature distribution and the feature distribution of the historical sample library is calculated; when the consistency of residual direction and the distance of feature distribution simultaneously meet the preset trigger conditions, the shared feature extraction parameters are frozen, and only the local branch parameters of the corresponding shore segment are updated; during the update, matching historical playback samples are selected, and parameter calibration is completed by combining the measured residual labels and the labels selected by confidence screening.

10. A storm surge forecasting system based on a coupled model, characterized in that, The system for implementing the storm surge forecasting method based on a coupled model as described in any one of claims 1 to 9 includes: The coupled forecast input module is used to obtain the forecast tide level, wind stress field, pressure field, astronomical tide component, and historical tide level residuals under the same tidal phase from the storm surge numerical coupling model. The spatial uniformity module is used to map the predicted tide level, wind stress field, pressure field, astronomical tide component and historical tide level residuals under the same tidal phase to multi-time multi-channel samples under the same effective coastal sea area grid. The shoreline constraint generation module is used to generate convolution constraint information based on the shoreline mask, the distance between the land and water boundaries, and changes in water depth. The residual correction module is used to input the multi-time multi-channel samples and convolutional constraint information into the convolutional neural network, perform shoreline constraint residual learning, and obtain the tide level residual correction amount; The fusion output module is used to generate residual confidence weights and impose anomaly restrictions on the tide level residual correction, then fuse them with the forecast tide level to output the storm surge forecast result.

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